1 Project Overview

In our previous two projects, we spent a great deal of time predicting income on the US census dataset. What we would like to determine in this project, is to see if the variables we determined important in predicting high or low income are important factors in association rule mining as well. Please refer to our second lab for more information. Previously, we have discovered that important predictor variables in classifying income level were:

• marriage status

• Male or Female

• age

• Hours per week

• Job role

• Education

In this study we will examine the same dataset through association rule mining. We will not only attempt to affirm our previously chosen factors that are associated with low or high income, but also look deeper into the relationships, and examine what levels of each factor are associated with high or low income.

We will perform a small ARM analysis and a large one while identifying relationships between both high and low income brackets with all the factors present in the dataset. We will then dive deeper, and perform ARM analysis on the relationships between all the factors of our dataset with high income bracket, and low income bracket individually, in an attempt to determine precisely what factors are associated with what income bracket. Finally, we will demonstrate an implementation of a grid search for the apriori algorithm, and propose upper and lower bounds for digestibility of a set of association rules, and demonstrate our process of selecting the strongest set of rules that we feel can be easily understood.

2 Business Understanding

• [10 points] Describe the purpose of the data set you selected (i.e., why was this data bcollected in the first place?). How will you measure the effectiveness of a good algorithm? Why does your chosen validation method make sense for this specific dataset and the stakeholders needs?

We chose this dataset from the UCI’s machine learning repository for its categorical predictive attributes. It contains 1994 Census data pulled from the US Census database. The prediction task we’ve set forth is to predict if a person salary range is >50k in a 1994, based on the various categorical/numerical attributes in the census database. The link to the data source is below:

https://archive.ics.uci.edu/ml/datasets/census+income

The effectiveness of our algorithm will be determined by support, confidence and lift. As these are the metrics that describe how strong a relationship between each element is with the other elements within each transaction. Currently, there are no methods for cross validation of association rules, although there are some hard working individuals out there that are attempting to create such a tool.

• TODO - ADD DEFINITION FOR LIFT/CONFIDENCE/SUPPORT HERE

3 Data Understanding

• [10 points] Describe the meaning and type of data (scale, values, etc.) for each attribute in the data file. Verify data quality: Are there missing values? Duplicate data? Outliers? Are those mistakes? How do you deal with these problems?
• [10 points] Visualize the any important attributes appropriately. Important: Provide an interpretation for any charts or graphs.

Here we will discuss each attribute and give some description about its ranges.

4 Setup

First, lets go ahead and load up necessary libraries:

Loaded Packages:
   arules, arulesViz, forcats, dplyr, plotly, data.table,
   pander, knitr, skimr, lubridate, ggplot2, cowplot,
   foreach, doParallel

Next, lets import our dataset

data <- read.csv("./data/adult-training.csv")

NA_sum <- sort(sapply(data, function(x) sum(is.na(x))), decreasing = TRUE)
data.frame((NA_sum))

GetFactors <- function(df) {
    return(names(Filter(is.factor, df)))
}
FixLevels <- function(x) {
    levels(x) <- trimws(levels(x))
    return(x)
}
data[GetFactors(data)] <- lapply(data[GetFactors(data)], FixLevels)
pander(lapply(data[GetFactors(data)], levels))

data$education <- fct_collapse(data$education, `No Diploma` = c("1st-4th", "5th-6th", 
    "7th-8th", "9th", "10th", "11th", "12th", "Preschool"), Associates = c("Assoc-acdm", 
    "Assoc-voc"), Diploma = c("Some-college", "HS-grad"))

data$income_bracket <- fct_collapse(data$income_bracket, small = "<=50K", large = ">50K")

levels(data$workclass)[levels(data$workclass) == "?"] <- "Other"
levels(data$occupation)[levels(data$occupation) == "?"] <- "Other-service"
levels(data$native_country)[levels(data$native_country) == "?"] <- "Other"
data[GetFactors(data)] <- lapply(data[GetFactors(data)], FixLevels)
pander(lapply(data[GetFactors(data)], levels))

data <- data[, -c(3, 5, 11:12)]
data$age <- cut(data$age, breaks = c(15, 25, 45, 65, 100), labels = c("Young", 
    "Middleaged", "Senior", "Retired"))
data$hours_per_week <- cut(data$hours_per_week, breaks = c(0, 20, 40, 60, 80), 
    labels = c("part-time", "full-time", "hard-working", "need-a-life"))
library(magrittr)
data %>% skim_to_list() %$% factor %>% select(-c("ordered", "missing", "complete")) %>% 
    kable

5 EDA

We’d also like to get a quick feel for the dataset through some visulizations.

p1 <- ggplot(data) + geom_bar(aes(x = age, fill = income_bracket), stat = "count") + 
    labs(x = "Age", y = "Count", title = "Age by Income", subtitle = "Histogram plot")
p1

Our first plot shows us a quick histogram of age groups and their income group. Not surprisingly, the majority of the “large” income group is in middleaged and senior groups supporting the common knowledge that as you get older, you should be making more money.

p2 <- ggplot(data, aes(x = education, fill = income_bracket, color = income_bracket)) + 
    geom_bar(alpha = 0.9, position = "fill") + coord_flip() + labs(x = "Education", 
    y = "Proportion", title = "Income bias based on Education", subtitle = "Stacked bar plot")
p2

Our next plot is a stacked bar chart of income group by density of education. We see here that higher education (Bachelors, Masters, Doctorate) yields a higher proportions of the “large” income bracket. Professional school also about equal with Docotorate suggesting specilaized trades and higher education are the best bet for making over 50k a year.

p3 <- ggplot(data, aes(x = marital_status, fill = income_bracket, color = income_bracket)) + 
    geom_bar(alpha = 0.9, position = "fill") + coord_flip() + labs(x = "Marital Status", 
    y = "Proportion", title = "Income bias based on Marital status", subtitle = "Stacked bar plot")
p3

Using the similar plot style as above, we’ll now look at income group by density of Marital Status. Which too no surprise to us researchers, married couples have a distinct advantage over those that are unmarried. In fact, the next highest categories are Widowed and Divorced. Which means, if you want to make more money in life, you should at least give marriage a try.

p4 <- ggplot(data, aes(x = occupation, fill = income_bracket, color = income_bracket)) + 
    geom_bar(alpha = 0.9, position = "fill") + coord_flip() + labs(x = "Occupation Status", 
    y = "Proportion", title = "Income bias based on Occupation status", subtitle = "Stacked bar plot")
p4

Next, we’ll compare income groups by density of Occupation. This revealed a few obvious, but also a few interesting results. Exec-managerial and Prof-specialty were the highest categories to no one’s surprise. Protective-serv, transport-moving and tech-support also show good density for making over 50k. Some of the lowest categories thought were Armed-Forces, and house-cleaning/services.

p6 <- ggplot(data, aes(occupation)) + geom_bar(aes(fill = education), width = 0.5) + 
    theme(axis.text.x = element_text(angle = 60, vjust = 0.5)) + labs(title = "Histogram of occupation with education binning", 
    subtitle = "Occupation and Educational")
p6

Lastly, we combine education and ocupation to see if we can notice any particular relationships between the two groups. What kind of educations to the people with large incomes have? Exec-managerial show a large amount of bachelor’s and masters degree’s, which means, more school definitely helps in that occupation. Prof-specialty shows the best range of educational sectors respresented but we found it interesting that prof-school wasn’t a larger representation here. This is probably due to prof-specialty being a wider category than some in that you can be a professional in alot of different occupational sectors.

Armed-forces have an extremely low amount of education information which also makes sense as most are recruited right out of high school. We would have expected to see a higher amount of Diploma’s given out in this group, but perhaps the information is just missing from this dataset.

Finally, we can set up our dataset as a transactional dataset to be in the proper data format for the Apriori algorithm:

data <- as(data, "transactions")
summary(data)

#> transactions as itemMatrix in sparse format with
#>  32561 rows (elements/itemsets/transactions) and
#>  102 columns (items) and a density of 0.1077805 
#> 
#> most frequent items:
#> native_country=United-States                   race=White 
#>                        29170                        27816 
#>         income_bracket=small            workclass=Private 
#>                        24720                        22696 
#>                  gender=Male                      (Other) 
#>                        21790                       231771 
#> 
#> element (itemset/transaction) length distribution:
#> sizes
#>    10    11 
#>   208 32353 
#> 
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   10.00   11.00   11.00   10.99   11.00   11.00 
#> 
#> includes extended item information - examples:
#>           labels variables     levels
#> 1      age=Young       age      Young
#> 2 age=Middleaged       age Middleaged
#> 3     age=Senior       age     Senior
#> 
#> includes extended transaction information - examples:
#>   transactionID
#> 1             1
#> 2             2
#> 3             3

6 Modeling and Evaluation

• Different tasks will require different evaluation methods. Be as thorough as possible when analyzing the data you have chosen and use visualizations of the results to explain the performance and expected outcomes whenever possible. Guide the reader through your analysis with plenty of discussion of the results. For this task, we chose Option B: Association Rule Mining.

Option B: Association Rule Mining

• Create frequent itemsets and association rules.

• Use tables/visualization to discuss the found results.

• Use several measure for evaluating how interesting different rules are.

• Describe your results. What findings are the most compelling and why?

Before we begin with our analysis, lets check out the rule frequencies within the dataset. We are looking for rules with support >= .2

itemFrequencyPlot(data, support = 0.2)

7 Rule mining

Next, lets mine some rules with the apriori algorithm, and then clean up redundant rules. We are still sorting out what to set the minsupp and minconf to.

zerules <- apriori(data, parameter = list(minlen = 2, supp = 0.2, conf = 0.15), 
    appearance = list(rhs = c("income_bracket=small", "income_bracket=large"), 
        default = "lhs"), control = list(verbose = F))
length(zerules)

#> [1] 91

redundant <- is.redundant(zerules)
zerules.pruned <- zerules[redundant == FALSE]
rulesorted <- sort(zerules.pruned, by = "lift", decreasing = TRUE)
length(rulesorted)

#> [1] 25

(quality(rulesorted))

inspectDT(rulesorted, caption = "Association Rules")

7.2 Plots

7.2.1 Scatterplot

plot(rulesorted, method = "scatterplot", measure = c("support", "lift"), shading = "confidence", 
    engine = "htmlwidget")

Scatter Plot

7.2.1.1 Discussion

This plot shows us each rule, with x axis as support and Y axis as lift. They are colored by confidence. This makes a nice little view of which rules were made from the most data. These may not always be the most interesting rules, but they are definitely the strongest ones. From looking at this, we can note a few strong, interesting associations.

• Females are associated with low income bracket

  • Conversely, being a male is (with low confidence) associated with a high income bracket.

• Not being married is strongly associated with a low income bracket

• High school diploma only is associated with low income

• Private/housekeeping/server jobs are associated with low income

• No family is also associated with low income

These strong rules are by no means earth-shattering, but they do tell us that we are looking in the right direction, as they agree with the (sometimes unfortunate) realities of the world we live in.

7.2.2 Balloon plot

plot(rulesorted, method = "graph", measure = "confidence", shading = "lift", 
    engine = "htmlwidget")

Balloon Plot

7.2.2.1 Discussion

The balloon plot is able to filter and zoom, which gives the ability to look through each income group and see what rules are feeding the analysis. Just by seperating out the large income bracket, we begin to see that married-civ-spouce has one of the highest lift scores. The next two highest were white and Male. Which follows suit with our above research as well.

In the small income bracket, we see rules such as (Never-married, fulltime), (female, private/housekeeper/server), (Private/housekeeper/server, never-married). This would begin to tell us that if you’re female, never-married and work full time, then you’re chances are higher for making under 50k.

7.2.3 Parallel plot

plot(rulesorted, method = "paracoord", measure = "confidence", shading = "lift", 
    control = list(reorder = T))

Parallel Plot

7.2.3.1 Discussion

The width of the arrows represents support and the color represents confidence. We can see a few interesting things here. First of all, we have a striking level of confidence that being married gets you a large income, and then also interestingly we see that working as a private worker/housekeeper/server is a part of a lot of the rules related to being in the low income bracket (You can see this by looking where all the rules converge on LHS order 1).

7.2.4 Two key plot

This plot is often used to discuss the relationship between the order of the rules and their support/confidence.

plot(rulesorted, method = "two-key plot", measure = "lift", shading = "confidence", 
    engine = "htmlwidget")

Two Key Plot

7.2.4.1 Discussion

We can find several interesting bits of information here. First, we see that we only produced one rule of order 4, a few rules of order 3, and a bunch of order 2. We also note that the area with high support and confidence (upper right, a bit of a sweet spot), is dominated by the shorter rules.

8 Alternate Rule Mining

After our first attempt at mining for rules, we’re going to relax our support to 0.1 and increase our confidence to 98% see what we get. Aftewards, we’ll target small and large incomes individually in order to see if we can isolate the itemsets that are going to be of highest influence.

rule2 <- apriori(data, parameter = list(minlen = 2, supp = 0.1, conf = 0.98), 
    appearance = list(rhs = c("income_bracket=small", "income_bracket=large"), 
        default = "lhs"), control = list(verbose = F))
length(rule2)

#> [1] 50

redundant <- is.redundant(rule2)
rulep <- rule2[redundant == FALSE]
rulesorted2 <- sort(rulep, by = "lift", decreasing = TRUE)
length(rulesorted2)

#> [1] 36

We can see that this time around we’ve generated 36 rule’s. We’ll put them through the same inspection and plots as previously to see if any other rules stand out or if we’re seeing more of the same.

head(quality(rulesorted2))

inspectDT(rulesorted2, caption = "Alternate Association Rules")

plot(rulesorted2, method = "scatterplot", measure = c("support", "lift"), shading = "confidence", 
    engine = "htmlwidget")

plot(rulesorted2, method = "graph", measure = "confidence", shading = "lift", 
    engine = "htmlwidget")

plot(rulesorted2, method = "two-key plot", measure = "confidence", shading = "lift", 
    engine = "htmlwidget")

9 Targeting Small and Large Income

rule_small <- apriori(data, parameter = list(minlen = 2, supp = 0.12, conf = 0.95), 
    appearance = list(rhs = c("income_bracket=small"), default = "lhs"), control = list(verbose = F))
length(rule_small)

#> [1] 45

redundant <- is.redundant(rule_small)
rulep <- rule_small[redundant == FALSE]
rulesorted_small <- sort(rulep, by = "lift", decreasing = TRUE)
length(rulesorted_small)

#> [1] 25

head(quality(rulesorted_small))

inspectDT(rulesorted_small)

plot(rulesorted_small, method = "scatterplot", measure = c("confidence", "support"), 
    shading = "lift", engine = "htmlwidget")

rule_large <- apriori(data, parameter = list(minlen = 2, supp = 0.05, conf = 0.55), 
    appearance = list(rhs = c("income_bracket=large"), default = "lhs"), control = list(verbose = F))
length(rule_large)

#> [1] 53

redundant <- is.redundant(rule_large)
rulep <- rule_large[redundant == FALSE]
rulesorted_large <- sort(rulep, by = "lift", decreasing = TRUE)
length(rulesorted_large)

#> [1] 15

head(quality(rulesorted_large))

inspectDT(rulesorted_large)

plot(rulesorted_large, method = "scatterplot", measure = c("confidence", "support"), 
    shading = "lift", engine = "htmlwidget")

10 Conclusion

11 Deployment

Be critical of your performance and tell the reader how you current model might be usable by other parties. Did you achieve your goals? If not, can you reign in the utility of your modeling?

• How useful is your model for interested parties (i.e., the companies or organizations that might want to use it)?

• How would your deploy your model for interested parties?

• What other data should be collected?

• How often would the model need to be updated, etc.?

Our current model, wouldn’t be a good option for a production environment. Granted, there is astounding amounts of transacational data out there that can benefit from apriori and associative rule mining. Due to the trial and error used to isolate various rules and itemsets. We’re not confident that a new dataset will have any similar behavior or show similar itemsets. It is probably best used for the 1990 data on which it was created.

Overall, i believe our group achieved the goals we set forth. We learned the process of associative rule mining, discovered new trends and validated those previously seen throughout our analysis of this dataset. We’re satisfied that we’ve created a useful model for anyone who was looking to analyze Census Data.

• Interested parties for this dataset could be activist, feminist, political campaigns, or others looking to change public policy through validation of its inhabitants characteristics. The model would theoretically work for other years of Census data (with light variable tweaking), it could also be applied to look for time series trends.

• Since our model doesn’t require long run times, one method would be to deploy an endpoint REST API. That way users could query for a prediction on income, then get the results back quickly and easily. Maintenance would be fairly low, so hosting it on an AWS instance might prove frugal and functional.

• Other data would consist of supplying other years of Census Data to see how if similar rulesets appear over time. Pairing this dataset with economic information could also prove beneficial as i’m sure the economy would influence unemployment rate, salaries in various industries, and a multitude of other factors that influence people’s income.

• Since we’re dealing with Census data, a yearly update of the model would be sufficient to maintain its usefulness.

12 Exceptional Work

For our exceptional work, we decided to try and optimize the number of rules produced in our apriori algorithm with the RHS being both low and high income. We decided to further optimize it by finding the ruleset which would provide us the highest average lift, while being digestible. To do that, we implemented a fully parallelized grid search.

x <- 1:99
conf <- supp <- x/100

init <- data.frame(conf = conf, supp = supp)
params <- expand.grid(init)
nrow(params)

#> [1] 9801

transactions <- data
search <- function(sup, con) {
    rules <- apriori(data = data, parameter = list(minlen = 2, conf = con, supp = sup), 
        appearance = list(rhs = c("income_bracket=small", "income_bracket=large"), 
            default = "lhs"), control = list(verbose = F))
    redundant <- is.redundant(rules)
    rulepruned <- rules[redundant == FALSE]
    rulelength <- length(rulepruned)
    return(data.frame(support = sup, conf = con, nrules = rulelength, avlift = mean(quality(rulepruned)$lift)))
}

library(parallel)
gs <- mcmapply(search, params[[1]], params[[2]], mc.cores = 12L, SIMPLIFY = F)
results <- do.call(rbind, gs)

libary(doParallel)
library(foreach)
numCores <- parallel::detectCores()
workers <- makeCluster(numCores - 1)
invisible(clusterEvalQ(workers, library(arules)))
registerDoParallel(workers)

results <- foreach(i = 1:nrow(params), .combine = rbind) %dopar% {
    search(params[i, 1], params[i, 2])
}

results %>% arrange(desc(avlift)) %>% filter(nrules <= 30) %>% filter(nrules >= 
    20) %>% filter(support > 0.15) %>% filter(conf > 0.15)

optimalRules <- apriori(data, parameter = list(conf = 0.18, supp = 0.32), appearance = list(rhs = c("income_bracket=small", 
    "income_bracket=large"), default = "lhs"), control = list(verbose = F))
sortedOptimalRules <- sort(optimalRules, by = "lift", decreasing = TRUE)
inspectDT(sortedOptimalRules)